WordNet records no synonym and no antonym for old boy network. It is the only member of its synset, which is common for technical, taxonomic and single-sense vocabulary — there is no other English word that means the same thing. The broader and narrower terms below are the useful relations in that case.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
an exclusive informal network linking members of a social class or profession or organization in order to provide connections and information and favors (especially in business or politics)
“professional women have developed an old boy network of their own”
Synonyms, antonyms and the broader and narrower relations for old boy network come from Princeton University’s WordNet. Full sources and licences.